# std::cosh, std::coshf, std::coshl

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< cpp‎ | numeric‎ | math

Defined in header `<cmath>` |  |
| (1) |
float cosh ( float num ); double cosh ( double num ); long double cosh ( long double num ); |  | (until C++23)
/*floating-point-type*/ cosh ( /*floating-point-type*/ num ); |  | (since C++23) (constexpr since C++26)
float coshf( float num ); | (2) | (since C++11) (constexpr since C++26)
long double coshl( long double num ); | (3) | (since C++11) (constexpr since C++26)
SIMD overload (since C++26) |  |
Defined in header `<simd>` |  |
template< /*math-floating-point*/ V > constexpr /*deduced-simd-t*/<V> cosh ( const V& v_num ); | (S) | (since C++26)
Additional overloads (since C++11) |  |
Defined in header `<cmath>` |  |
template< class Integer > double cosh ( Integer num ); | (A) | (constexpr since C++26)

1-3) Computes the hyperbolic cosine of num. The library provides overloads of `std::cosh` for all cv-unqualified floating-point types as the type of the parameter.(since C++23)

S) The SIMD overload performs an element-wise `std::cosh` on v_num. (See `math-floating-point` and `deduced-simd-t` for their definitions.) | (since C++26)

A) Additional overloads are provided for all integer types, which are treated as double. | (since C++11)

### Parameters

num | - | floating-point or integer value

### Return value

If no errors occur, the hyperbolic cosine of num (cosh(num), or

enum +e-num
2

) is returned.

If a range error due to overflow occurs, +HUGE_VAL, `+HUGE_VALF`, or `+HUGE_VALL` is returned.

### Error handling

Errors are reported as specified in math_errhandling.

If the implementation supports IEEE floating-point arithmetic (IEC 60559),

- if the argument is ±0, 1 is returned.
- If the argument is ±∞, +∞ is returned.
- if the argument is NaN, NaN is returned.

### Notes

For the IEEE-compatible type double, if |num| > 710.5, then std::cosh(num) overflows.

The additional overloads are not required to be provided exactly as (A). They only need to be sufficient to ensure that for their argument num of integer type, std::cosh(num) has the same effect as std::cosh(static_cast<double>(num)).

### Example

Run this code

    #include <cerrno>
    #include <cfenv>
    #include <cmath>
    #include <cstring>
    #include <iostream>
    // #pragma STDC FENV_ACCESS ON

    int main()
    {
        const double x = 42;

        std::cout << "cosh(1) = " << std::cosh(1) << '\n'
                  << "cosh(-1) = " << std::cosh(-1) << '\n'
                  << "log(sinh(" << x << ")+cosh(" << x << ")) = "
                  << std::log(std::sinh(x) + std::cosh(x)) << '\n';

        // special values
        std::cout << "cosh(+0) = " << std::cosh(0.0) << '\n'
                  << "cosh(-0) = " << std::cosh(-0.0) << '\n';

        // error handling
        errno=0;
        std::feclearexcept(FE_ALL_EXCEPT);

        std::cout << "cosh(710.5) = " << std::cosh(710.5) << '\n';

        if (errno == ERANGE)
            std::cout << "    errno == ERANGE: " << std::strerror(errno) << '\n';
        if (std::fetestexcept(FE_OVERFLOW))
            std::cout << "    FE_OVERFLOW raised\n";
    }

Possible output:

    cosh(1) = 1.54308
    cosh(-1) = 1.54308
    log(sinh(42)+cosh(42)) = 42
    cosh(+0) = 1
    cosh(-0) = 1
    cosh(710.5) = inf
        errno == ERANGE: Numerical result out of range
        FE_OVERFLOW raised

### See also

sinhsinhfsinhl (C++11)(C++11) | computes hyperbolic sine (\({\small\sinh{x}}\)sinh(x)) (function)
tanhtanhftanhl (C++11)(C++11) | computes hyperbolic tangent (\({\small\tanh{x}}\)tanh(x)) (function)
acoshacoshfacoshl (C++11)(C++11)(C++11) | computes the inverse hyperbolic cosine (\({\small\operatorname{arcosh}{x}}\)arcosh(x)) (function)
cosh(std::complex) | computes hyperbolic cosine of a complex number (\({\small\cosh{z}}\)cosh(z)) (function template)
cosh(std::valarray) | applies the function std::cosh to each element of valarray (function template)
C documentation for cosh

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